1. The manager of a paint supply store wants to determine whether the mean amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer actually is 1 gallon. It is known from the manufacturer’s specifications that the standard deviation of the amount of paint is equal to 0.02 gallon. A random sample of 50 cans is selected, and the mean of the amount of paint per 1-gallon can is found to be .995 gallon.
a. Is there evidence that the mean amount is different from 1.0 gallon (use a=0.01)?
b. Compare the p-value and interpret its meaning.
c. Construct a 99% confidence interval estimate of the population mean amount of paint.
d. Compare the results of (a) and (c). What conclusions do you reach?
2. If you use a 0.05 level of significance in a two tail hypothesis test, what will decide if zstat = -0.76?
3. The quality- control manager at a light bulb factory needs to determine whether the mean life of a large shipment of light bulbs is equal to 375 hours. The population standard deviation is 100 hours. A random sample of 64 light bulbs indicates a sample mean life of 350 hours.
a. At the 0.05 level of significance, is there evidence that the mean life is different from 375 hours?
b. Compute the p- value and interpret its meaning.
c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs.
d. Compare the results of ( a) and ( c). What conclusions do you reach?
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